A solid sphere rolls down two different inclined planes of the same height but of different inclinations

Options

A. In both cases, the speeds and time of descent will be same
B. The speeds will be different but time of descent will be same
C. Speeds will be same but time of descent will be different
D. The speeds and time of descent will be different

Answer

A

Explanation

`As, v =sqrt((2gh)/(1+(1)/(MR^(3))))` Hence velocity is independent of inclination of the plane and depends only on height h through which body descends.
But because `t=(1)/(sin theta) t = (1)/(sin theta)sqrt((2h)/(g)(1+(I)/(MR^(3))))` depends on the inclination also,k here greater the inclination leaser will be the time of descend. Hence, in present case, the spedd will be same (because h is same) but time of descend will be different (because different inclinations)